Division by zero mathematical inconsistencies

[fcabouat]

Hi,

In Elm repl I get :

-1 / 0 == 1 / -0
False : Bool

Which is a bit weird mathematically and comes from the fact that 1 / 0 gives Infinity where it should (imho) give NaN.

cheers,

François

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[bitamar]

Hi @fcabouat,
I don't find it inconsistent - Division by zero is either infinity, or -infinity, so if "-0" is the same as 0, that's the expected result. I.e -1 / 0 is -Infinity and 1 / 0 is Infinity.

[bitamar]

Hi @fcabouat,
I don't find it inconsistent - Division by zero is either infinity, or -infinity, so if "-0" is the same as 0, that's the expected result. I.e -1 / 0 is -Infinity and 1 / 0 is Infinity.

[fcabouat]

-(1 / x) == -1 / x == 1 / -x for every x != 0. Breaking that rule for x = 0 is indeed an inconsistency.

At least in real numbers space dividing by zero is a mathematical error / is undefined. It's not equal to Infinity or -Infinity. Otherwise, it would lead to -Infinity == Infinity. Is it what you're proposing ?

What about Elm's policy of making errors explicit / forcing the programmer to handle those errors in a type safe way ?

[fcabouat]

-(1 / x) == -1 / x == 1 / -x for every x != 0. Breaking that rule for x = 0 is indeed an inconsistency.

At least in real numbers space dividing by zero is a mathematical error / is undefined. It's not equal to Infinity or -Infinity. Otherwise, it would lead to -Infinity == Infinity. Is it what you're proposing ?

What about Elm's policy of making errors explicit / forcing the programmer to handle those errors in a type safe way ?

[fcabouat]

After some research, it appears I'm not the only one to cringe about this mathematical inconsistency.
Anyway, since the same behavior can be seen in Haskell & al and has been standardized in IEEE 754, I guess t wouldn't be much wiser to go against the standard.

Leaving https://stackoverflow.com/questions/9354016/division-by-zero-in-haskell as a reference and closing the issue.

[fcabouat]

After some research, it appears I'm not the only one to cringe about this mathematical inconsistency.
Anyway, since the same behavior can be seen in Haskell & al and has been standardized in IEEE 754, I guess t wouldn't be much wiser to go against the standard.

Leaving https://stackoverflow.com/questions/9354016/division-by-zero-in-haskell as a reference and closing the issue.